There are no part-time (or even full time) Ph.D. programs at top universities in computer science or mathematics that can be completed by those who work full time. For various personal reasons I find myself in a position that requires me to work full time; however, I am passionate about theoretical computer science/mathematics. Unfortunately, most American schools do not accommodate Ph.D. students under these circumstances. Is this a decision based upon the assumption that those who work full time will not produce good/enough work, or is this a decision based, simply, upon the fact that professors want to work standard hours and teaching a course from 5:30 - 6:20 is quite non-standard?Courses are not a major issue. The course requirements for a Ph.D. usually do not significantly differ than those for a Masters and many universities offer a Masters program in computer science for full-time workers. I do see two other major barriers to a part-time Ph.D.: Funding and Research.
Nearly all Ph.D. student get funded for tuition and some living expenses via a fellowship, teaching assistantship or research assistantship. Government agencies generally don't give fellowships to part-time students and a TA or RA requires about twenty hours a week, leaving someone who already has a full-time job with no time for actually completing the Ph.D.
But suppose you felt that a Ph.D. was worth the expense or were independently wealthy and for some reason still had to work a full-time job. Ph.D. level research in math and theoretical computer science requires intense background study and long stretches of thinking, understanding the problem and working through many different ideas until one actually makes significant progress toward original work. For this one needs time and the relationship is not linear. Someone who can spend forty hours a week focusing on research will be far more than twice as successful as one who can only spend twenty.
The dominant limitation on number of Ph.D. students in CS departments is funding. If you have a record that would have gotten you in to a top computer science department as a full-time Ph.D. student and you bring your own money to the table, I suspect at many schools you can work out a part-time schedule. But you'll find doing original research on a part-time basis a daunting if not impossible task.